A non-local model for cancer stem cells and the tumor growth paradox

Abstract

The tumor growth paradox refers to the observation that incomplete treatment of cancers can enhance their growth. As shown here and elsewhere, the existence of cancer stem cells (CSC) can explain this effect. CSC are less sensitive to treatments, hence any stress applied to the tumor selects for CSC, thereby increasing the fitness of the tumor. In this paper we use a mathematical model to understand the role of CSC in the progression of cancer. Our model is a rather general system of integro-differential equations for tumor growth and tumor spread. Such a model has never been analysed, and we prove results on local and global existence of solutions, their uniqueness and their boundedness. We show numerically that this model exhibits the tumor growth paradox for all parameters tested. This effect becomes more relevant for small renewal rate of the CSC.